An optimization model to estimate the air travel demand for the United States

Worldwide, air travel demand has greatly increased and historical travel demand data is essential for air transportation planning, policy-making and market evaluation. However, historical air travel demand is not always available or complete and oftentimes must be estimated. To address this problem, we present a non-linear optimization model to estimate the historical air travel demand between origin and destination (OD) airports in the United States (US). In contrast to existing models, our model estimates itinerary-level OD demand served by air carriers while considering travelers' choice behaviors. The model formulation is based on a logit model along with observed data. To consider travelers' choice behaviors, an observed utility is assigned to each itinerary. The utility is a function of factors such as fare, flight time, number of connections, and departure and arrival times. Travelers between an OD pair are assumed to choose itineraries that have maximum utility. In the optimal solution, the demand between an OD pair distributes among the itineraries connecting the OD pair by a logit model. An evolutionary strategy is used to calibrate the model parameters such that the model estimates match sample results from the Airline Origin and Destination Survey as close as possible. This method solves a least square parameter estimation model and our model iteratively until the parameter estimation is stabilized. To make the demand estimation consistent with observed data, the statistics from the Airline Origin and Destination Survey, T100 Domestic Market data, and Official Airline Guide are used to create the constraints in the model. An efficient iterative balancing algorithm is used to solve the optimization model. The algorithm iteratively maximizes the dual of the model along directions defined by unit vectors and keeps some first order optimality conditions satisfied. We applied the model to estimate the travel demand served by seven major US carriers in a large-size US network. The network contains 457airports and about 200,000 itineraries. We compared with our estimation results with the statistics from the American Travel Survey. The comparisons are done at national level and state level respectively. Our comparisons suggest that the demand estimation produced by our model is generally consistent with those statistics.